Computation, Dynamics, and Cognition

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Oxford University Press, May 29, 1997 - Philosophy - 192 pages
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Currently there is growing interest in the application of dynamical methods to the study of cognition. Computation, Dynamics, and Cognition investigates this convergence from a theoretical and philosophical perspective, generating a provocative new view of the aims and methods of cognitive science. Advancing the dynamical approach as the methodological frame best equipped to guide inquiry in the field's two main research programs--the symbolic and connectionist approaches--Marco Giunti engages a host of questions crucial not only to the science of cognition, but also to computation theory, dynamical systems theory, philosophy of mind, and philosophy of science. In chapter one Giunti employs a dynamical viewpoint to explore foundational issues in computation theory. Using the concept of Turing computability, he precisely and originally defines the nature of a computational system, sharpening our understanding of computation theory and its applications. In chapter two he generalizes his definition of a computational system, arguing that the concept of Turing computability itself is relative to the kind of support on which Turing machine operate. Chapter three completes the book's conceptual foundation, discussing a form of scientific explanation for real dynamical systems that Giunti calls "Galilean explanation." The book's fourth and final chapter develops the methodological thesis that all cognitive systems are dynamical systems. On Giunti's view, a dynamical approach is likely to benefit even those scientific explanations of cognition which are based on symbolic models. Giunti concludes by proposing a new modeling practice for cognitive science, one based on "Galilean models" of cognitive systems. Innovative, lucidly-written, and broad-ranging in its analysis, Computation, Dynamics, and Cognition will interest philosophers of science and mind, as well as cognitive scientists, computer scientists, and theorists of dynamical systems. This book elaborates a comprehensive picture of the application of dynamical methods to the study of cognition. Giunti argues that both computational systems and connectionist networks are special types of dynamical systems. He shows how this dynamical approach can be applied to problems of cognition, information processing, consciousness, meaning, and the relation between body and mind.
  

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Contents

Mathematical Dynamical Systems and Computational Systems
3
2 Mathematical dynamical systems
7
3 Computational systems
12
4 The emulation relation
23
5 Reversible versus irreversible systems
28
6 The realization relation
37
7 Virtual systems the reversible realizability of irreversible systems and the existence of reversible universal systems
42
Proofs of selected theorems
46
6 Galilean frameworks of Ksystems
120
7 Explicit versus implicit specification of the set of state transitions of a possible Galilean model of a Ksystem
124
8 The inductive method for constructing Galilean frameworks of Ksystems
129
9 The deductive method for constructing Galilean frameworks of Ksystems
131
Proofs of selected theorems
133
Notes
137
Cognitive Systems and the Scientific Explanation of Cognition
139
2 Cognitive systems as dynamical systems
140

Notes
50
Generalized Computational Systems
55
2 Turing machines on pattern field F
57
3 Is the concept of computability on pattern field F reducible to the usual concept of Turing computability?
67
4 Is a nonrecursive pattern field necessary for computing nonrecursive functions?
78
5 The concept of computability on pattern field F is a generalization of the usual concept of computability
83
6 Computational systems on pattern field F
88
Proofs of selected theorems
92
Notes
106
Galilean Models and Explanations
113
2 Real dynamical systems versus mathematical dynamical systems
114
3 Models of Ksystems
115
4 Galilean explanations and the traditional practice of dynamical modeling
116
5 Galilean explanations are based on Galilean models of Ksystems
119
the argument
141
computation theory and dynamical systems theory
145
31 Dynamical systems theory and the explanation of cognition based on symbolic models
146
32 Computation theory and the explanation of cognition based on neural networks or other continuous dynamical models
148
4 Cognitive systems and their models
153
41 Simulation models of cognitive systems
154
42 Galilean models of cognitive systems
155
Pexplanatory and correct Galilean frameworks of cognitive systems
158
44 The Galilean approach to cognitive science
159
Notes
160
References
163
Index
173
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